1. Field of the Invention
The present invention generally relates to a process simulating method, a process simulator, and a recording medium for recording a process simulation program. More specifically, the present invention is directed to such a process simulating method for simulating an oxidation process in a semiconductor device manufacturing step for an LSI and the like. Also, the present invention is directed to a process simulator for the above-described process simulating method, and also to a recording medium for recording a process simulation program.
2. Description of the Related Art
Conventionally, process simulators are practically available in order to predict internal physical amounts and shapes such as impurity profiles of various elements for constituting semiconductor devices such as LSIs by calculating an oxidation process, a diffusion process, an ion implantation process in manufacturing steps of these LSIs with employment of computers. When such a process simulator is employed, manufacturing processes of the respective elements for constituting the semiconductor device such as the LSI can be optimized as a desk plan in such a manner that the semiconductor device such as the LSI has a desirable electric characteristic. As a consequence, the manufacturing cost can be considerably reduced and the time can be largely shortened, as compared with the actual manufacture of the semiconductor device as a trial case.
To calculate the manufacturing steps for the various sorts of elements by using the computer, the model formulae have been installed in the process simulator with respect to each of the processes. Among these processes, as to the oxidation process, for example, the following simulation method is known. That is, the formula of Deal-Grove (see formula (22)) disclosed in Japanese publication xe2x80x9cVLSI Designing/Manufacturing Simulationxe2x80x9d written by M. MORISUE issued by CMC K. K., in 1987, pages 62 to 63 is differentiated with respect to time to thereby obtain the formula (23). Then, this formula (23) is solved to simulate the temporal change in the film thickness of the silicon oxide film (SiO2, simply referred to as an xe2x80x9coxide filmxe2x80x9d hereinafter).
In the formulae (22) and (23), symbol xe2x80x9ctxe2x80x9d indicates a time instant in the oxidation process, symbol xe2x80x9cTOXxe2x80x9d shows a film thickness of an oxide film at a present time instant, and symbol xe2x80x9cTPOXxe2x80x9d indicates a film thickness of an oxide film at a preceding time instant, and also symbols xe2x80x9cAxe2x80x9d and xe2x80x9cBxe2x80x9d are parameters related to oxidation speed. The formula (23) is applied to an one-dimensional oxidation case such that a flux of an oxidizing agent does not depend upon a place:
TOX2+ATOX=B(t+xcfx84)xe2x80x83xe2x80x83(22)
                                          ⅆ                          T              OX                                            ⅆ            t                          =                  B                      (                                          2                ⁢                                  T                  OX                  P                                            +              A                        )                                              (        23        )            
On the other hand, very recently, in connection with the high integration in semiconductor devices such as LSIs and VLSIs, namely in conjunction with very fine structures of structural elements for constituting these semiconductor devices, these structural elements are isolated by employing LOCOS (Local Oxidation of Silicon) structures and trench structures in order to avoid electrical adverse influences caused by these structural elements. As a consequence, also in process simulators, oxide film shapes in these LOCOS structures and trench structures are required to be simulated. When these oxide film shapes are simulated, since fluxes of oxidizing agents differ from each other, depending on places, the simulation for the oxide film shapes should be carried out at least in the two-dimensional manner, which is completely different from the one-dimensional oxidation.
The two-dimensional oxidation simulation as to the LOCOS structure is disclosed in Japanese publication xe2x80x9cSemiconductor Process Device Simulation Techniquexe2x80x9d written by S. ISOMAE, published by REALIZE publisher, in 1990, on pages 79 to 89. Also, the method for determining the time step xe2x80x9cxcex94txe2x80x9d equal to the unit time of the oxidizing agent diffusion within the oxide film during the oxidation process is described in xe2x80x9cTwo-Dimensional Oxidationxe2x80x9d by DAEJE CHIN et al., IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-30, No. 7, July 1983.
Now, the conventional two-dimensional oxidation process simulating method disclosed in the last-mentioned publication will be described with reference to a flow chart shown in FIG. 5 and a sectional structure view of an LSI under manufacture indicated in FIG. 6.
In the flow chart of FIG. 5, at the first step SA1, the time instant variable xe2x80x9ctxe2x80x9d used to count up a time elapse in the oxidation process is set to zero. Subsequently, the simulating operation is advanced to the step SA2. At this step SA2, the Laplace equation indicated in the above-described formula (24) as to the oxide film 1 is solved to calculate oxidizing agent (oxidant) density CSOX at the boundary surface between the oxide film 1 and the silicon substrate 2 (will be referred to as xe2x80x9ca boundary surface between an oxide film/a silicon substratexe2x80x9d hereinafter). Then, the simulating operation is advanced to the further step SA3. In the following formula (24), symbol DOX shows the diffusion coefficient of the oxidizing agent within the oxide film 1:
DOX∇2COX=0xe2x80x83xe2x80x83(24).
At the step SA3, the film thickness TSOX of the oxide film 1 of the side wall in the LOCOS structure at the time instant xe2x80x9ctxe2x80x9d is calculated. Thereafter, the process operation is advanced to the step SA4.
At the step SA4, the calculated value of this film thickness TSOX is substituted for the below-mentioned formula (25) so as to calculate the time step xe2x80x9cxcex94txe2x80x9d equal to the unit time of the oxidizing agent diffusion within the oxide film 1 during the oxidation process. Subsequently, the simulating process is advanced to the step SA5. It should be understood that symbol xe2x80x9cxcex94TOXxe2x80x9d shown in the formula (25) is a desirable film thickness increase amount of the oxide film 1 per 1 time step xcex94t. This formula (25) is substantially same as the formula [23] disclosed in page 748 of the last-mentioned publication xe2x80x9cTwo-Dimensional Oxidationxe2x80x9d.                               Δ          ⁢                      xe2x80x83                    ⁢          t                =                              (                                                            2                  ⁢                                      T                    OX                    S                                                  +                A                            B                        )                    ⁢          Δ          ⁢                      xe2x80x83                    ⁢                      T            OX                                              (        25        )            
At the step SA5, the time instant xe2x80x9ctxe2x80x9d is advanced only by the time step xcex94t. In other words, after the time step xcex94t is added to the time instant variable xe2x80x9ctxe2x80x9d, this simulating process is advanced to the step SA6.
At this step SA6, after the calculation is made of deformation in the shape of the oxidation film as to the time instant xe2x80x9ctxe2x80x9d, the simulating process is advanced to the further step SA7.
At this step SA7, the judgment is made as to whether or not the time instant xe2x80x9ctxe2x80x9d reaches an ending time instant of the oxidation process. If the judgment result is xe2x80x9cNOxe2x80x9d, then the simulating process is returned to the step SA2, at which the process operations defined from the step SA2 to the step SA6 are repeatedly performed. Then, in the case that the time instant xe2x80x9ctxe2x80x9d has reached the ending time instant of the oxidation process, since the judgement result of the step SB8 becomes xe2x80x9cYESxe2x80x9d, a series of simulation work is accomplished.
As previously explained, in accordance with the conventional process simulating method, as indicated in FIG. 6, the time step xe2x80x9cxcex94txe2x80x9d is determined in such a manner that the increased value of the film thickness TSOX of the oxide film of the side wall in the LOCOS structure is continuously made equal to the film thickness xcex94TOX.
On the other hand, in the above-explained conventional process simulating method, the film thickness TSOX of the side wall in the LOCOS structure is employed as the present film thickness of the oxide film 1 which is required to determine the time step xe2x80x9cxcex94txe2x80x9d. As a consequence, this conventional process simulating method owns such a drawback that this process simulating method cannot be applied to any of the oxidation process simulation methods. That is, when the respective structural elements for constituting a semiconductor device such as an LSI own arbitrary shapes other than the LOCOS structure, this conventional oxidation process simulating method cannot be used to simulate this oxidation process.
The present invention has been made to solve the above-described problem, and therefore, has an object to provide a process simulating method, a process simulator, and a recording medium for recording a process simulation program, capable of properly calculating a time step in an oxidation process even when the respective structural elements for constituting a semiconductor device such as an LSI own arbitrary shapes.
To achieve the above-described object, a process simulating method, as recited in claim 1 of the present invention, is featured by such a process simulating method for simulating an oxidation process in a step for manufacturing a semiconductor device, comprising: a first step in which a two-dimensional Laplace equation related to an oxidizing agent diffusion within an oxide film is solved to thereby calculate oxidizing agent concentration CSOX at a boundary surface between an oxide film/a silicon substrate; a second step in which the oxidizing agent density CSOX is substituted for the below-mentioned formula (1) so as to calculate an effective film thickness of the oxide film as to all of a plurality of preset modes on the boundary surface between the oxide film/the silicon substrate; the formula (1) is defined by such that equilibrium oxidizing agent concentration within the oxide film is xe2x80x9cC*xe2x80x9d, an oxidation reaction coefficient at the boundary surface between the oxide film/the silicon substrate is xe2x80x9ckxe2x80x9d, a mass transfer coefficient at a boundary surface between an atmosphere/an oxide film is xe2x80x9chxe2x80x9d, a diffusion coefficient of an oxidizing agent within the oxide film is xe2x80x9cDxe2x80x9d, and a parameter related to an oxidation speed is equal to xe2x80x9cAxe2x80x9d given by the below-mentioned formula (2):                                           T            OX            E                    =                                    A              2                        ·                                                                                h                                          h                      +                      k                                                        ·                                      C                    *                                                  -                                  C                  OX                  S                                                            C                OX                S                                                    ,        and                            (        1        )                                          A          =                      2            ⁢                          D              ⁡                              (                                                      1                    h                                    +                                      1                    k                                                  )                                                    ;                            (        2        )            
a third step for calculating a minimum value TMOX of the film thickness TEOX; and a fourth step in which both the minimum value TMOX and a desirable film thickness increase amount xcex94TOX of the oxide film per a time step xcex94t are substituted for the below-mentioned formula (3) to thereby calculate the time step xe2x80x9cxcex94txe2x80x9d, the time step xe2x80x9cxcex94txe2x80x9d being equal to unit time of the oxidizing agent diffusion within the oxide film in the oxidation process;                                           Δ            ⁢                          xe2x80x83                        ⁢            t                    =                                    (                                                                    2                    ⁢                                          T                      OX                      M                                                        +                  A                                B                            )                        ⁢            Δ            ⁢                          xe2x80x83                        ⁢                          T              OX                                      ,                            (        3        )            
wherein: another parameter B related to an oxidation speed, expressed in a right hand of the above-described formula (3), is given by the below-mentioned formula (4), and symbol xe2x80x9cN1xe2x80x9d shown in a right hand of the below-mentioned formula (4) is a parameter determined by an oxidation sort:                     B        =                                            2              ⁢              D              ⁢                              xe2x80x83                            ⁢                              C                *                                                    N              1                                .                                    (        4        )            
Also, to achieve the above-described object, a process simulating method, as recited in claim 2 of the present invention, is featured by the process simulating method according to claim 1 wherein: the process simulating method is comprised of, instead of the fourth step, a fifth step in which the minimum value TMOX, a maximum film thickness increase amount xcex94TMMOX and also a minimum film thickness increase amount xcex94TMOX with respect to the oxide film thickness increase amount xcex94TOX, and a preceding time step xcex94tP are substituted for the below-mentioned formula (5) related to a maximum time step xcex94tMM, the below-described formula (6) related to a minimum time step xcex94tM, and the below-mentioned formula (7) directed to such a time step xcex94t which should be calculated when a ratio of a present time step to the preceding time step xcex94tP is assumed as xe2x80x9cRxe2x80x9d, whereby the time step xcex94t is calculated:                               Δ          ⁢                      xe2x80x83                    ⁢                      t            MM                          =                              (                                                            2                  ⁢                                      T                    OX                    M                                                  +                A                            B                        )                    ⁢          Δ          ⁢                      xe2x80x83                    ⁢                      T            OX            MM                                              (        5        )                                          Δ          ⁢                      xe2x80x83                    ⁢                      t            M                          =                              (                                                            2                  ⁢                                      T                    OX                    M                                                  +                A                            B                        )                    ⁢          Δ          ⁢                      xe2x80x83                    ⁢                      T            OX            M                                              (        6        )            xe2x80x83xcex94t=max{xcex94tM,min(xcex94tPxc3x97R,xcex94tM)}xe2x80x83xe2x80x83(7).
Furthermore, a process simulator, as recited in claim 3 of the present invention, is featured by such a process simulator for simulating an oxidation process in a step for manufacturing a semiconductor device, comprising: first means in which a two-dimensional Laplace equation related to an oxidizing agent diffusion within an oxide film is solved to thereby calculate oxidizing agent concentration CSOX at a boundary surface between an oxide film/a silicon substrate; second means in which the oxidizing agent density CSOX is substituted for the below-mentioned formula (8) so as to calculate an effective film thickness of the oxide film as to all of a plurality of preset modes on the boundary surface between the oxide film/the silicon substrate; the formula (8) is defined by such that equilibrium oxidizing agent concentration within the oxide film is xe2x80x9cC*xe2x80x9d, an oxidation reaction coefficient at the boundary surface between the oxide film/the silicon substrate is xe2x80x9ckxe2x80x9d, a mass transfer coefficient at a boundary surface between an atmosphere/an oxide film is xe2x80x9chxe2x80x9d, a diffusion coefficient of an oxidizing agent within the oxide film is xe2x80x9cDxe2x80x9d, and a parameter related to an oxidation speed is equal to xe2x80x9cAxe2x80x9d given by the below-mentioned formula (9):                                           T            OX            E                    =                                    A              2                        ·                                                                                h                                          h                      +                      k                                                        ·                                      C                    *                                                  -                                  C                  OX                  S                                                            C                OX                S                                                    ,        and                            (        8        )                                          A          =                      2            ⁢                          D              ⁡                              (                                                      1                    h                                    +                                      1                    k                                                  )                                                    ;                            (        9        )            
third means for calculating a minimum value TMOX of the film thickness TEOX; and fourth means in which both the minimum value TMOX and a desirable film thickness increase amount xcex94TOX of the oxide film per a time step xcex94t are substituted for the below-mentioned formula (10) to thereby calculate the time step xe2x80x9cxcex94txe2x80x9d, the time step xe2x80x9cxcex94txe2x80x9d being equal to unit time of the oxidizing agent diffusion within the oxide film in the oxidation process;                                           Δ            ⁢                          xe2x80x83                        ⁢            t                    =                                    (                                                                    2                    ⁢                                          T                      OX                      M                                                        +                  A                                B                            )                        ⁢            Δ            ⁢                          xe2x80x83                        ⁢                          T              OX                                      ,                            (        10        )            
wherein: another parameter B related to an oxidation speed, expressed in a right hand of the above-described formula (10), is given by the below-mentioned formula (11), and symbol xe2x80x9cN1xe2x80x9d shown in a right hand of the below-mentioned formula (11) is a parameter determined by an oxidation sort:                     B        =                                            2              ⁢              D              ⁢                              xe2x80x83                            ⁢                              C                *                                                    N              1                                .                                    (        11        )            
Also, to achieve the above-described object, a process simulator, as recited in claim 4 of the present invention, is featured by the process simulator according to claim 3 wherein: the process simulator is comprised of, instead of the fourth means, fifth means in which the minimum value TMOX, a maximum film thickness increase amount xcex94TMMOX and also a minimum film thickness increase amount xcex94TMOX with respect to the oxide film thickness increase amount xcex94TOX, and a preceding time step xcex94tP are substituted for the below-mentioned formula (12) related to a maximum time step xcex94tMM, the below-described formula (13) related to a minimum time step xcex94tM, and the below-mentioned formula (14) directed to such a time step xcex94t which should be calculated when a ratio of a present time step to the preceding time step xcex94tP is assumed as xe2x80x9cRxe2x80x9d, whereby the time step xcex94t is calculated:                               Δ          ⁢                      xe2x80x83                    ⁢                      t            MM                          =                              (                                                            2                  ⁢                                      T                    OX                    M                                                  +                A                            B                        )                    ⁢          Δ          ⁢                      xe2x80x83                    ⁢                      T            OX            MM                                              (        12        )                                          Δ          ⁢                      xe2x80x83                    ⁢                      t            M                          =                              (                                                            2                  ⁢                                      T                    OX                    M                                                  +                A                            B                        )                    ⁢          Δ          ⁢                      xe2x80x83                    ⁢                      T            OX            M                                              (        13        )            xe2x80x83xcex94t=max{xcex94tM,min(xcex94tPxc3x97R,xcex94tM)}xe2x80x83xe2x80x83(14).
Also, to achieve the above-described object, a process simulator, as recited in claim 5 of the present invention, is featured by the process simulator according to claim 3 wherein: the process simulator is arranged by a computer including at least: a memory unit for previously storing thereinto a program to simulate the oxidation process of the semiconductor device manufacturing step; and a central processing unit for controlling the operations of the first to fourth means, and the memory unit.
Moreover, a recording medium, as recited in claim 6 of the present invention, is featured by such a recording medium for recording thereon a process simulation program used to simulate an oxidation process in a step for manufacturing a semiconductor device, wherein: the process simulation program causes a computer to execute: a first step in which a two-dimensional Laplace equation related to an oxidizing agent diffusion within an oxide film is solved to thereby calculate oxidizing agent concentration CSOX at a boundary surface between an oxide film/a silicon substrate; a second step in which the oxidizing agent density CSOX is substituted for the below-mentioned formula (15) so as to calculate an effective film thickness of the oxide film as to all of a plurality of preset modes on the boundary surface between the oxide film/the silicon substrate; the formula (15) is defined by such that equilibrium oxidizing agent concentration within the oxide film is xe2x80x9cC*xe2x80x9d, an oxidation reaction coefficient at the boundary surface between the oxide film/the silicon substrate is xe2x80x9ckxe2x80x9d, a mass transfer coefficient at a boundary surface between an atmosphere/an oxide film is xe2x80x9chxe2x80x9d, a diffusion coefficient of an oxidizing agent within the oxide film is xe2x80x9cDxe2x80x9d, and a parameter related to an oxidation speed is equal to xe2x80x9cAxe2x80x9d given by the below-mentioned formula (16):                                           T            OX            E                    =                                    A              2                        ·                                                                                h                                          h                      +                      k                                                        ·                                      C                    *                                                  -                                  C                  OX                  S                                                            C                OX                S                                                    ,        and                            (        15        )                                          A          =                      2            ⁢                          D              ⁡                              (                                                      1                    h                                    +                                      1                    k                                                  )                                                    ;                            (        16        )            
a third step for calculating a minimum value TMOX of the film thickness TEOX; and a fourth step in which both the minimum value TMOX and a desirable film thickness increase amount xcex94TOX of the oxide film per a time step xcex94t are substituted for the below-mentioned formula (17) to thereby calculate the time step xe2x80x9cxcex94txe2x80x9d, the time step xe2x80x9cxcex94txe2x80x9d being equal to unit time of the oxidizing agent diffusion within the oxide film in the oxidation process;                                           Δ            ⁢                          xe2x80x83                        ⁢            t                    =                                    (                                                                    2                    ⁢                                          T                      OX                      M                                                        +                  A                                B                            )                        ⁢            Δ            ⁢                          xe2x80x83                        ⁢                          T              OX                                      ,                            (        17        )            
wherein: another parameter B related to an oxidation speed, expressed in a right hand of the above-described formula (17), is given by the below-mentioned formula (18), and symbol xe2x80x9cN1xe2x80x9d shown in a right hand of the below-mentioned formula (18) is a parameter determined by an oxidation sort:                     B        =                                            2              ⁢              D              ⁢                              xe2x80x83                            ⁢                              C                *                                                    N              1                                .                                    (        18        )            
Also, to achieve the above-described object, a recording medium, as recited in claim 7 of the present invention, is featured by the recording medium for recording thereon a process simulation program, according to claim 6, wherein: the process simulating method is comprised of, instead of the fourth step, a fifth step in which the minimum value TMOX, a maximum film thickness increase amount xcex94TMMOX and also a minimum film thickness increase amount xcex94TMOX with respect to the oxide film thickness increase amount xcex94TOX, and a preceding time step tP are substituted for the below-mentioned formula (19) related to a maximum time step xcex94tMM, the below-described formula (20) related to a minimum time step xcex94tM, and the below-mentioned formula (21) directed to such a time step xcex94t which should be calculated when a ratio of a present time step to the preceding time step xcex94tP is assumed as xe2x80x9cRxe2x80x9d, whereby the time step xcex94t is calculated:                               Δ          ⁢                      xe2x80x83                    ⁢                      t            MM                          =                              (                                                            2                  ⁢                                      T                    OX                    M                                                  +                A                            B                        )                    ⁢          Δ          ⁢                      xe2x80x83                    ⁢                      T            OX            MM                                              (        19        )                                          Δ          ⁢                      xe2x80x83                    ⁢                      t            M                          =                              (                                                            2                  ⁢                                      T                    OX                    M                                                  +                A                            B                        )                    ⁢          Δ          ⁢                      xe2x80x83                    ⁢                      T            OX            M                                              (        20        )            xe2x80x83xcex94t=max{xcex94tM,min(xcex94tPxc3x97R,xcex94tM)}xe2x80x83xe2x80x83(21).